How to join two faces
Selecting the top edge of the trapezium is most easily done in Vertex mode - select both ends and switch back to Edge mode. But even then, TinyCad is a bit of a long way round, here. 

Vertices must somehow be cut (topologically) into the bottom edge of the rectangle, so alternatives include:


With Snap set to 'Active' and 'Vertex' and Automerge switched on:
AltD duplicate the bottom vertices of the rectangle in their edge, and drag them any old where..
Snap them onto the top vertices of the trapezium




On the whole though, when modeling, you would want the extra edges in the rectangle. If so..


CtrlR and scroll, cut 2 edge-loops into the rectangle
With Snap and Automerge set as before, and your Pivot set to 'Median', in Vertex mode, with one of the new loop vertices active...
SX the new loops, snapping to one of the top vertices of the trapezium.




These are by no means the 'right' ways of doing this.. I'm sure you have/will have your own grab-bag of favorite modeling patterns.